EP0493057A1 - Increased frequency resolution in a synthesizer - Google Patents

Abstract

A direct digital frequency sythesizer increases the frequency resolution of the analog output signal by using fractionalization techniques. The best integer value IFR (200) of a digital signal is determined and the next integer value IFR + 1 of a digital signal is used to determine a weighted fractionalized value of the digital signal. The fractionalized value of the digital signal is used to synthesize the analog output signal having increased frequency resolution. In addition, IFR and IFR + 1 are optimally distributed during the weighting process to ensure a minimum cumulative phase error.

The synthesizer is particularly well suited for use in a radio transceiver, for instance in a digital radiotelephone system where a NRZ data stream modulates a carrier signal by employing phase critical modulation techniques such as GMSK.

Description

Field of the Invention
• This invention relates generally to frequency synthesizers and more particularly to a direct digital synthesizer incorporating fractionalization to increase frequency resolution.
Background of the Invention
• With radiotelephone systems moving into digital data transfer instead of audio-type data transfer, direct digital synthesis is an ideal adaptation of converting analog technology into digital technology. In a direct digital synthesizer (DDS), a known non-return to zero (NRZ) data stream representing a predetermined sequence is input into a DDS modulator resulting in a corresponding analog signal. The analog signal can either be modulated or unmodulated depending on the NRZ data stream representation.
• The DDS is ideal and very well suited for use in the transmitters of digital radiotelephone systems. These transmitters generally require high stability and increased frequency accuracy than do their typical analog counterparts. Reproducability of a typical quadrature modulated signal is also a problem in the transmitters of digital radiotelephone systems. Using analog-to-analog synthesizers typically leads to various adjustments required for such things as DC offset and input analog signal amplitude adjustment. With DDS modulators incorporated in the transmitters of digital radiotelephone system, the requirements of stability and reproducability are inherent in the DDS modulator itself.
• Due to the requirements of wide frequency coverage and fine frequency resolution, phase accumulators that are typically employed in DDS modulators generally are required to be quite long. This requirement comes about due to the fact that more bits are required to realize the fine frequency resolution that digital radiotelephone systems require. Large phase accumulators tend to make transmitter circuitry complex which in turn may become very expensive. Also, to minimize part count and ensure the use of common parts throughout the radiotelephone system, an engineering compromise must be made as to the type and quantity of parts that are used.
• Thus, a need exists for a direct digital synthesizer having an increased effective frequency resolution without increasing phase accumulator length, thus making the DDS hardware simpler and frequency modulation easier to implement.
Summary of the Invention
• A frequency synthesizer increases the frequency resolution of an analog output signal, the analog output signal being synthesized in accordance with a digital control signal. The frequency synthesizer provides a first digital input signal for a first predetermined time period A and a second digital input signal for a second predetermined time period B and generates the weighted average of the first digital input signal and the second digital input signal to produce the digital control signal.
Brief Description of the Drawings
• FIG. 1 generally depicts a digital radiotelephone transmitter which may employ the present invention.
• FIG. 2 generally illustrates a direct digital synthesizer (DDS) in accordance with the invention.
• FIG. 3 generally depicts a DDS modulator in accordance with the invention.
Detailed Description of a Preferred Embodiment
• FIG. 1 generally depicts a digital radiotelephone transmitter that may employ the present invention. The transmitter 100 is comprised of a controller 105 which essentially receives data from external equipment and distributes the data to the appropriate section in the transmitter 100. The controller 105 may be a microprocessor such as a Motorola 6800 and may also include a digital signal processor (DSP) such as a Motorola 68030. Continuing, the controller 105, having received data from external equipment, distributes non-return to zero (NRZ) data 110 to a DDS modulator 115. The NRZ data essentially represents voice data which a transmitter 100 receives from external equipment and is required to transmit to a user. The DDS modulator 115 receives the NRZ data and generates an analog output signal which is input into an exciter 120, which is essentially a low power amplifier. The controller 105 controls the exciter 120 depending upon the required output. A power amplifier 125 receives the output from the exciter 120 and amplifies the radio frequency (RF) signal which is then output over a typical antenna 130.
• FIG. 2 generally depicts a direct digital synthesizer (DDS) in accordance with the present invention. The DDS has as input a P-bit word which represents a phase increment/frequency word and is called I _FR 200. I_FR 200 is input into a phase accumulator 210 which also has as input a clock frequency given by F_CLK 205. In the preferred embodiment, P is a 16-bit long word and F _CLK 205 is 35.1 MHz. The phase accumulator 210 accepts the 16-bit word I_FR 200 where the input is put in to a P-bit register 225, again where P is 16 in the preferred embodiment. The clock signal F _CLK 205 clocks in the signal I_FR 200 into the register 225 which then outputs the signal I_FR 200 into a conventional adder 230. In this manner, the required phase corresponding to the integer value of I_FR 200 is generated by the phase accumulator 210. Output of the phase accumulator 210 is a 16-bit phase word which is input into a phase-to-amplitude converter 215. The phase-to-amplitude converter 215 is essentially a converter which takes the sine of the phase word. The phase-to-amplitude converter 215, which in the preferred embodiment is a typical ROM, stores a look-up table which has a predetermined amplitude output for a corresponding phase word input. The predetermined amplitude output of the desired signal is then input into a digital-to-analog converter 220 which transforms the amplitude output into an analog output signal.
• The DDS shown in FIG. 2 has limited resolution particularly due to the clock signal F _CLK 205 and the length of the register 225 in the phase accumulator 210. With this in mind, the smallest phase resolution achievable by the DDS is $${\text{⌀}}_{\text{RES}}{\text{= 2π/2}}^{\text{P}}\text{radians}$$

  

  and the smallest frequency step achievable by the DDS is $${\text{F}}_{\text{RES}}{\text{= F}}_{\text{CLK}}{\text{/2}}^{\text{P}}\text{Hz}$$

  

  which intuitively makes sense since F_CLK is the maximum frequency that can be achieved and 2^P is the largest integer value that can be achieved with a P-bit phase increment/frequency word. The phase accumulator 210 increment value is given by $${\text{Δ⌀ = ⌀}}_{\text{RES}}{\text{x I}}_{\text{FR}}$$

  

  again where I _FR 200 is the phase increment/frequency word applied to the phase accumulator 210 input. With these equations in hand, the output frequency of the DDS is given by $${\text{F}}_{\text{DDS}}{\text{= Δ⌀/ΔT = (I}}_{\text{FR}}{\text{)(F}}_{\text{RES}}{\text{) = (F}}_{\text{CLK}}{\text{)(I}}_{\text{FR}}{\text{/2}}^{\text{P}}\text{) Hz.}$$

  

  From these results, it is apparent that for a fixed F _CLK 205, increased frequency resolution can only be achieved by increasing the number of bits in the phase increment/frequency I_FR 200.
• This invention overcomes the above mentioned limitation by varying the I _FR 200 value between two adjacent states. This generates an average DDS output frequency which has an effective I_FR value with a fractional part. This fraction process can be described as follows. Assume that the fractionalization is controlled by some constant rate, F, which is an arbitrary integer divisor of F_CLK and < F_CLK/2. F_FRACT is chosen to be < F_CLK/2 to ensure at least one accumulation of the I_FR or I_FR + 1 value for that fractionalization interval, the fractionalization interval given by $${\text{T}}_{\text{FRACT}}{\text{=1/F}}_{\text{FRACT}}\text{.}$$

  

  Furthermore, defining $${\text{I}}_{\text{FRACT}}{\text{=I}}_{\text{FR}}\text{+ N/D}$$

  

  where I is the integer portion of the fractional frequency word and N and D are the numerator and denominator of the fractional part respectively, the frequency resolution is increased by a factor of D and is given by $${\text{F}}_{\text{RES}}{\text{=F}}_{\text{CLK}}{\text{/(D x 2}}^{\text{P}}\text{) Hz.}$$

  

  This fractional process is achieved by cycling through a fractional period which consists of D fractional intervals During this period, I_FR is set to I+1 for N fractional intervals and set to I for the remaining D-N intervals.
• The concept of weighting the value of I_FR for a fractionalized interval is best explained by example. Assume that the analog output signal is required to be 7.200000 MHZ ± 2 Hz. Based on the parameters of the preferred embodiment, namely P = 16 and F_CLK = 35.1 MHz, the best value for I_FR = 13443, which results in the following output frequency $${\text{F}}_{\text{DDS}}{\text{= (F}}_{\text{CLK}}{\text{)(I}}_{\text{FR}}{\text{/2}}^{\text{P}}\text{) Hz = 7.199849 MHz}$$

  

  In order to achieve the desired frequency accuracy, fractionalization was implemented using the following parameters: IFR = 13443, N = 72 and D = 256. Thus $${\text{I}}_{\text{FRACT}}\text{= 13443 + (72/256) = 13443.28125}$$

  

  and $${\text{F}}_{\text{DDS}}{\text{= (F}}_{\text{CLK}}{\text{)(I}}_{\text{FRACT}}{\text{/2}}^{\text{P}}\text{) Hz = 7.1999996 Hz}$$

  

  which exhibits a frequency error of 0.4 Hz. I_FRACT is essentially a weighted average of I_FR and I_FR + 1, where I_FR has been applied to the phase accumulator 210 for 72 of the 256 possible cycles and I_FR + 1 has been applied for the remaining 184 cycles. As can be seen, incorporating fractionalization techniques significantly increases the frequency resolution of the DDS.
• Since the integer value of I_FR represents the rate at which phase is accumulated in the phase accumulator 210, it makes sense that I_FR + 1 will accumulate phase faster than I_FR. In digital radiotelephone systems employing phase critical modulation techniques such as Gaussian Minimum Shift-Keying (GMSK) or equivalent alternatives, accumulated phase error must be accounted for and minimized. If all I_FR states were sent to the phase accumulator 210 first, a large accumulated phase error would occur at the output of the accumulator 210. Likewise, if the remaining I_FR + 1 were then sent to the accumulator 210, the accumulated phase error would decrease but would then increase again toward the end of the I_FR + 1 state. With the above mentioned technique of increasing frequency resolution, the peak accumulated phase error over the fractional period can be minimized by optimally distributing I_FR and I_FR + 1.
• FIG. 3 depicts implementation of the DDS into a DDS modulator in accordance with the invention. The NRZ data, which in the preferred embodiment is at a rate of 270.8333 KHz, enters a modulation control box 310. The modulation control box 310 contains a microprocessor, such as a Motorola 6800, and a conventional ROM in the preferred embodiment. The minimization of accumulated phase error is performed by software running in the microprocessor in the modulation control box 310. Recalling that F_FRACT is required to be an integer divisor of F_CLK and < F_CLK/2, F_FRACT is chosen to be 8 times the NRZ data rate or 270.8333 KHz, resulting in a F_FRACT = 2.1666 MHz. Minimization is achieved by starting with the I_FR state during the first T_FRACT period, which in the preferred embodiment is 1/F_FRACT or .462 µs, and incrementing I_FR to the I_FR + 1 state when the accumulated phase error over the fractional period has exceeded $${\text{⌀}}_{\text{RES}}{\text{x (F}}_{\text{CLK}}{\text{/F}}_{\text{FRACT}}\text{) °}$$

  

  which is .0879° in the preferred embodiment. This has the effect of distributing the I_FR and I_FR + 1 states as evenly across the fractional period as possible. Using values from the example above, the phase error associated with the I_FR state can be calculated on a per T_FRACT basis $${\text{⌀}}_{\text{ERROR}}{\text{= [(F}}_{\text{DESIRED}}{\text{-(F}}_{\text{RES}}{\text{I}}_{\text{FR}}{\text{)](T}}_{\text{FRACT}}\text{)(360) °}$$

  

  or $${\text{⌀}}_{\text{ERROR}}\text{=[(7.2 MHz - (535.58 Hz x IFR)](.1663ms) °}$$

  

  which for IFR results in $${\text{⌀}}_{\text{ERROR IFR}}\text{= 0.0251°}$$

  

  and for IFR +1 results in $${\text{⌀}}_{\text{ERROR IFR +1}}\text{= -0.0640°.}$$

  

  The process begins by applying the I_FR state to the accumulator 210 during the first T_FRACT interval, which results in a cumulative phase error of 0.0251° which is less than 0.0879°, thus the I_FR state will be applied to the accumulator 210 during the second T_FRACT interval. The process repeats until the cumulative phase error is greater than the 0.0879° limit, which happens after the fourth T_FRACT interval. After the fourth T_FRACT interval, the cumulative phase error is 0.1004°, thus the I_FR + 1 state will be sent during the fifth T_FRACT interval. The phase error for the fifth T_FRACT interval is -0.0640° but the cumulative phase error is decreased from 0.1004° to 0.0364° by subtracting ⌀_{ERROR IFR +1} for the fifth T_FRACT interval. Since the cumulative phase error is now below the 0.0879° limit, the I_FR state will again be applied to the accumulator during the sixth T_FRACT interval. The minimization process repeats until all the I_FR and I_FR + 1 states have been applied to the accumulator.
• The technique used to minimize the cumulative phase error can also be applied using the same approach but employing I_FR and I_FR-1 states or any other combination of states that achieve equivalent results. The technique, as described in the example with no modulation, also increases the frequency resolution when modulation is required, since the only difference is the NRZ data stream. In this manner, frequency resolution is increased without the need for longer registers in the phase accumulator 210 or alteration of the clock frequency F _CLK 205 used as a reference. The technique also allows for minimization of the cumulative phase error during the fractionalization process which in turn yields a more accurate modulation.

Claims (10)

1. A frequency synthesizer having increased frequency resolution of an analog output signal, the analog output signal being synthesized in accordance with a digital control signal, the frequency synthesizer characterized by:
      means for providing a first digital input signal for a first predetermined time period A and a second digital input signal for a second predetermined time period B; and
      means, coupled to said means for providing, for generating the weighted average of said first digital input signal and said second digital input signal to produce the digital control signal.
2. The frequency synthesizer of claim 1 wherein said means for providing a first digital input signal for a first predetermined time period A and a second digital input signal for a second predetermined time period B is further characterized by means for providing a first digital input signal having an integer value representing a first phase change value for a first predetermined time period A and a second digital input signal having an integer value representing a second phase change value for a second predetermined time period B.
3. The frequency synthesizer of claim 2 wherein said means for providing is further characterized by means for subdividing said first predetermined time period A and said second predetermined time period B into N samples such that (A/N + B/N) = 1.
4. The frequency synthesizer of claim 3 wherein said means for weighting is further characterized by means for accumulating said first phase change value and said second phase change value to produce an accumulated phase value.
5. The frequency synthesizer of claim 4 wherein said means for weighting is further characterized by means, responsive to said means for accumulasting, for distributing said first predetermined time period A samples and said second predetermined time period B samples to minimize said accumulated phase value.
6. A radio transceiver incorporating a direct digital frequency synthesizer which synthesizes an analog output signal, the radio transceiver characterized by:
      means for providing a digital signal corresponding to the frequency of the analog output signal;
      means, coupled to said means for providing, for generating a first integer value for a first predetermined time period and for generating a second integer value for a second predetermined time period;
      means for generating the weighted average of said first integer value and said second integer value to produce a first non-integer value;
      means for providing a reference signal having a fixed frequency;
      means, coupled to said means for generating and said means for providing the weighted average, for synthesizing the analog output signal;
      means for providing a plurality of radio frequency signals; and
      means, coupled to said means for synthesizing and said means for providing a plurality of radio frequency signals, for transmitting one of said plurality of radio frequency signals having a frequency related to said analog output signal.
7. The radio transceiver of claim 6 wherein said means for generating a first integer value for a first predetermined time period A and a second integer value for a second predetermined time period B is further characterized by means for generating a first integer value representing a first phase change value for a first predetermined time period A and a second integer value representing a second phase change value for a second predetermined time period B and means for subdividing said first predetermined time period A and said second predetermined time period B into N samples such that (A/N + B/N) = 1.
8. The radio transceiver of claim 6 wherein said means for weighting is further characterized by means for accumulating said first phase change value and said second phase change value to produce an accumulated phase value and means, responsive to said means for accumulating, for distributing said first predetermined time period A samples and said second predetermined time period B samples to minimize said accumulated phase value.
9. A method of increasing the frequency resolution of an analog output signal in a frequency synthesizer, the analog output signal being synthesized in accordance with a digital control signal, the method characterized by:
      providing a first digital input signal for a first predetermined time period A and a second digital input signal for a second predetermined time period B; and
      generating, coupled to said step of providing, the weighted average of said first digital input signal and said second digital input signal to produce the digital control signal.
10. A method of increasing the frequency resolution of an analog output signal in a frequency synthesizer, the analog output signal being synthesized in accordance with a digital input signal, the method characterized by:
       providing a digital signal corresponding to the frequency of the analog output signal;
       generating, coupled to said step of providing, a first integer value for a first predetermined time period A and generating a second integer value for a second predetermined time period B;
       generating the weighted average of said first integer value and said second integer value to produce a first non-integer value;
       providing a reference signal having a fixed frequency; and
       synthesizing, coupled to said step of generating and said step of providing a reference signal, the analog output signal.

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